Theory and Numerical Modelling of the Effects of Ablator Wall and Hohlraum Transfer Gas Thermal Resistances on Deuterium-Tritium Redistribution Rates

Abstract

The influence of capsule wall material and the transfer gas surrounding the capsule on the time required for beta-heating-induced redistribution of a 50-50 mole percent mixture of deuterium and tritium (DT) in a spherical capsule are investigated analytically and numerically. The derivation of an analytical solution for the redistribution time in a one-dimensional binary diffusion model, which includes the thermal resistance of the capsule, is first described. This result shows that the redistribution time for a high conductivity capsule wall is approximately doubled after 8 days of 3He formation. In contrast, with a low thermal conductivity capsule wall (e.g., polyimide), the redistribution time would increase by less than 10%The substantial effect of the capsule wall resistance suggested that the resistance to heat transfer from the capsule through the surrounding transfer gas to the hohlraum wall would also influence the redistribution process. This was investigated with a spherical model, which was based on accounting for energy transfer by diffusion with a conduction heat transfer approximation. This made it possible to solve for the continuous temperature distribution throughout the capsule and surrounding gas. As with the capsule the redistribution times depended on the relative values of the thermal resistances of the vapor in the capsule and the transfer gas. With increasing vapor thermal resistance (increased concentration of 3He) redistributions times for hydrocarbon capsules were less than the minimum one-dimensional value of 27 minutes. Further analytical and experimental investigation of the thermal interaction between the capsule and hohlraum is recommended.